Course Syllabus

Biostatistics 830 (Special Topic)

Stochastic Models in Survival Analysis

 

Winter 2016 (3 Credits)

 

Instructor:

Alex Tsodikov

Professor of Biostatistics

M4142 SPH II

Phone: 734-615-6416

E-mail: tsodikov@umich.edu

Class web: Canvas

 

Time and place:

Tuesday and Thursday 10-11:30pm M1170 (Moved from M1122)

School of Public Health II

 

Outline

This class is about semiparametric statistical models for a survival time driven by a latent variable or a random process. They include survival models motivated by a model of the disease progression such as cancer, models where a proportion of the subjects never develop the event of interest (cure models), multivariate survival models based on Copulas, models for sequential and competing events some of which could be unobserved, etc. In the univariate survival setting we will look at transformation models. In the context of survival models with a missing random variable (so-called frailty models), the transformation is induced by an unobserved mixing random variable (a frailty). In a more general setting the transformation functional is induced by an unobserved stochastic process affecting the hazard function. Shared frailty and processes can been used to model correlated (multivariate) survival data with the transformation linked to the models of dependence, Copulas. Asymptotics and statistical inference algorithms for the models will be considered using modern estimators that provide efficient NPMLE solutions and are amenable to martingale machinery. Various applications, mostly in cancer, will be studied.

 

Literature and course materials:

Two sets of electronic class notes prepared using a tablet PC and generally covering the same material will be made available as the primary reading. One set of notes will be systematic and one will be made on the fly during the class.

 

Recommended reading:

Much of the material is so new that it is only available in research papers and manuscripts. They will be posted on Canvas. There are many books that touch upon one or the other particular aspect, and they will be introduced during the course.

 

Prerequisites:

BIOSTAT 601, 602, 675

875 (highly recommended)

 

Homework:

3-4 homeworks will be given throughout the course

 

Project:

A choice of a review paper or a data analysis project will be given as a final course assignment. A list of potential topics will be given. Students are encouraged to append the list and propose topics related to their thesis work.

 

Exams: No exams

 

Grade: Attendance: 20%; Homework: 40%; Project: 40%

 

Competencies

 

1. Understand the various concepts of model building and related theory of Laplace transform of a random variable and a random process.

 

2. Master univariate frailty models and track their relationship to transformation and cure models.

 

3. Understand survival models driven by a stochastic process.

 

4. Master development of efficient estimating equations and their algorithmic solutions such as the EM algorithm and the weighted Breslow algorithms.

 

5. Understand and model dependence using a shared variable or process and their relationship to Copulas.

 

6. Characterize local and global dependence using a variety of dependence measures.

 

7. Critique and summarize the state of the field.